Find the modulus of each of the following complex numbers and hence

= sin(90° + 30° ) - icos(90° + 30°)

$=\cos 30^{\circ}+i \sin 30^{\circ}$

Since, sin(90°+ α) = cosα

And cos(90° + α) = -sinα

$=\frac{\sqrt{3}}{2}+i \frac{1}{2}$

Hence it is of the form

$\mathrm{Z}=\frac{\sqrt{3}}{2}+i \frac{1}{2}=\mathrm{r}(\cos \theta+i \sin \theta)$

Therefore r = 1

Hence its modulus is 1 and argument is $\frac{\pi}{6}$.